Some remarks on the dyadic Rademacher maximal function

Mikko Kemppainen. "Some remarks on the dyadic Rademacher maximal function." Colloquium Mathematicae 131.1 (2013): 113-128. <http://eudml.org/doc/283966>.

@article{MikkoKemppainen2013,
abstract = {Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) $L^\{p\}$ inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on ℝⁿ. In addition, to compensate for the lack of an $L^∞$ inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.},
author = {Mikko Kemppainen},
journal = {Colloquium Mathematicae},
keywords = {R-bound; dyadic cube; Rademacher maximal function; RMF property},
language = {eng},
number = {1},
pages = {113-128},
title = {Some remarks on the dyadic Rademacher maximal function},
url = {http://eudml.org/doc/283966},
volume = {131},
year = {2013},
}

TY - JOUR
AU - Mikko Kemppainen
TI - Some remarks on the dyadic Rademacher maximal function
JO - Colloquium Mathematicae
PY - 2013
VL - 131
IS - 1
SP - 113
EP - 128
AB - Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) $L^{p}$ inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on ℝⁿ. In addition, to compensate for the lack of an $L^∞$ inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.
LA - eng
KW - R-bound; dyadic cube; Rademacher maximal function; RMF property
UR - http://eudml.org/doc/283966
ER -